Related papers: On the hermiticity of q-differential operators and…
Examples are given of non-Hermitian Hamiltonian operators which have a real spectrum. Some of the investigated operators are expressed in terms of the generators of the Weil-Heisenberg algebra. It is argued that the existence of an…
Quasi-Hermitian quantum systems, including $\mathcal{PT}$-symmetric ones, can be mapped to equivalent Hermitian systems via a similarity transformation that redefines the inner product with a positive-definite metric operator. Although an…
The focus of this work is a correspondence between the Hilbert space operators on one hand, and doubly periodic generalized functions on the other. The linear map that implements it, referred to as the Q-transform, enables a direct…
Recently, much research has been carried out on Hamiltonians that are not Hermitian but are symmetric under space-time reflection, that is, Hamiltonians that exhibit PT symmetry. Investigations of the Sturm-Liouville eigenvalue problem…
Noncommutative differential calculus on quantum Minkowski space is not separated with respect to the standard generators, in the sense that partial derivatives of functions of a single generator can depend on all other generators. It is…
We start from Wootter's construction of discrete phase spaces and Wigner functions for qubits and more generally for finite dimensional Hilbert spaces. We look at this framework from a non-commutative space perspective and we focus on the…
A very well known result by Harish-Chandra claims that any Hermitian symmetric space of non-compact type admits a canonical embedding into a complex vector space $V$. The image of this embedding is a bounded symmetric domain in $V$. This…
The calculation of realistic N-body wave functions for identical fermions is still an open problem in physics, chemistry, and materials science, even for N as small as two. A recently discovered fundamental algebraic structure of many-body…
We construct the rings of generalized differential operators on the ${\bf h}$-deformed vector space of ${\bf gl}$-type. In contrast to the $q$-deformed vector space, where the ring of differential operators is unique up to an isomorphism,…
A new combinatorial approach to the ribbon tableaux generating functions and q-Littlewood Richardson coefficients of Lascoux, Leclerc and Thibon is suggested. We define operators which add ribbons to partitions and following Fomin and…
We present explicit formulae for q-exponentials on quantum spaces which could be of particular importance in physics, i.e. the q-deformed Minkowski-space and the q-deformed Euclidean space with two, three or four dimensions. Furthermore,…
We prove that the Hermite functions are an absolute Schauder basis for many global weighted spaces of ultradifferentiable functions in the matrix weighted setting and we determine also the corresponding coefficient spaces, thus extending…
In a recent paper [15], Hilbert space operators $T$ with the property that each sequence of the form $\{\|T^n h\|^2\}_{n=0}^{\infty}$ is conditionally positive definite in a semigroup sense were introduced. In the present paper, this line…
Many basis sets for electronic structure calculations evolve with varying external parameters, such as moving atoms in dynamic simulations, giving rise to extra derivative terms in the dynamical equations. Here we revisit these derivatives…
Quantum operations (QO) describe any state change allowed in quantum mechanics, such as the evolution of an open system or the state change due to a measurement. We address the problem of which unitary transformations and which observables…
This is the second part of a paper about a q-deformed analog of non-relativistic Schroedinger theory. It applies the general ideas of part I and tries to give a description of one-particle states on q-deformed quantum spaces like the…
On conformal manifolds of even dimension $n\geq 4$ we construct a family of new conformally invariant differential complexes. Each bundle in each of these complexes appears either in the de Rham complex or in its dual. Each of the new…
For a non-Hermitian Hamiltonian H possessing a real spectrum, we introduce a canonical orthonormal basis in which a previously introduced unitary mapping of H to a Hermitian Hamiltonian h takes a simple form. We use this basis to construct…
To develop a unitary quantum theory with probabilistic description for pseudo- Hermitian systems one needs to consider the theories in a different Hilbert space endowed with a positive definite metric operator. There are different…
We study Fourier theory on quantum Euclidean space. A modified version of the general definition of the Fourier transform on a quantum space is used and its inverse is constructed. The Fourier transforms can be defined by their Bochner's…